Electrochemistry

In electrolytic hydrogen production, the cell voltage increases with increasing reversible voltage. This is mainly caused by overvoltages and parasitic currents, which generate

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gy losses and limit the cell efficiency. The cell voltage is the sum of the reversible voltage and additional overvoltages appearing in the cell (Ursúa et al. 2012a)

𝑈_cell = 𝑈_rev+ 𝑈_ohm+ 𝑈_act+ 𝑈_con, (2.10)

where Ucell is the cell voltage, Uohm the overpotential due to ohmic losses in the cell ele-ments, Uact the activation overvoltage, and Ucon refers to the concentration overvoltage.

The ohmic losses in water electrolysis are related to wastage of electrical energy in the form of heat formation according to the Ohm’s law and are proportional to the electric cur-rent. The opposition of the ions flow of the electrolyte, the formation of the gas bubbles on the electrode surfaces, and the diaphragm are also a part of the electrical resistance. The dominant ohmic losses are the ionic losses caused by the electrolyte. For alkaline electroly-sis, the area specific ionic resistance can be calculated from (Milewski et al. 2014)

𝑟_ion𝑠 = 𝛿_el

𝜎_𝑒𝑙(𝑇, 𝑀), (2.11)

where δel is the thickness of the electrolyte layer and σel the ionic conductivity of the alka-line solution as a function of temperature T and molarity M. In proton exchange membrane (PEM) electrolysis, the ionic losses are calculated similarly to (2.11) by dividing the mem-brane thickness by the conductivity of the memmem-brane (García-Valverde et al. 2012).

The activation voltage is overvoltage in the electrodes caused by the electrode kinetics.

Even when the necessary reversible voltage is supplied, the electrode reactions are at zero or inherently slow. The charge between the chemical species and the electrodes has to be overcome and it depends on the catalytic properties of the electrode materials. The anodic half-reaction produces a higher activation overvoltage (Uact,a) than the half-reaction at the cathode (Uact,b). The activation overvoltage is nonlinear with respect to the electric current passing through the cell and can be calculated from the Butler-Volmer equation (Milewski et al. 2014)

𝑖 = 𝑖₀[𝑒^{(𝑅𝑇𝑧𝐹𝑈𝛼a act,a)}− 𝑒^{(𝑅𝑇𝑧𝐹𝑈𝛼c act,c)}], (2.12) where i is the current density, i0 the exchange current density, and αa/c the charge-transfer coefficients. The charge-transfer coefficients describe the share of the energy barrier be-tween the electrodes and are dependent on the temperature. The exchange current density

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is strongly dependent on the materials and the geometry of the electrodes. The Butler-Volmer equation can be approximated using the logarithmic Tafel equation (Hammoudi et al. 2012)

𝑈_act,a/c= 2.3026 𝑅𝑇

𝑧𝐹𝛼_a/clog (𝑖

𝑖₀). (2.13)

The last term of the sum (2.10), the concentration voltage Ucon, is caused by mass transport processes. Transport limitations reduce reactant concentration of the products in the inter-face between the electrode and the electrolyte. Usually, the concentration overvoltage is much lower than Uohm and Uact (Ursúa et al. 2012a). Exemplary overvoltages excluding the concentration overvoltage are illustrated in Fig. 2.6.

Fig. 2.6 Exemplary overvoltages as a function of current density in alkaline electrolysis at T = 75 °C and p = 30 bar. Main parameters used in simulation are presented in Appendix 1. Concentration overvoltage Ucon was not included in simulations.

The overvoltages presented in (2.10) can be expressed as related resistances. These sistances can then be presented in a corresponding electrical circuit of series connected re-sistances illustrated in Fig. 2.7.

Fig. 2.7 A simplified circuit analogy of a water electrolysis system (Zeng & Zhang 2010).

Rbubble,O2

R1 Ranode Rmembrane Rions Rbubble,H2 Rcathode R’1

+

-e

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R1 and R’1 are the electrical resistances of the wirings and connections at the anode and cathode, respectively. Ranode and Rcathode originate from the overpotentials of the oxygen and hydrogen evolution reactions on the surfaces of the electrodes. Rbubble,O2 and Rbubble,H2 are the resistances due to gas bubble formation, which hinder the contact between the elec-trodes and the electrolyte. Rions and Rmembrane resistances originate from the electrolyte (Zeng & Zhang 2010).

2.2.1 Transport resistances

Convective mass transfer plays an essential role in the ionic transfer, heat dissipation and distribution, and gas bubbles’ behaviour in the electrolyte. The viscosity and flow field of the electrolyte determine the ionic mass transfer, temperature distribution and bubble sizes, bubble detachment and rising velocity, and hence influence the current and potential distri-butions in the electrolytic cell. During the water electrolysis process the concentration of the electrolyte increases resulting in increased viscosity. Water is usually continuously added to the system to maintain a constant concentration of the electrolyte. Greater mass transfer results in greater reaction rates, but on the downside leads to increased gas bubble formation, which can hinder the contact between the electrodes and the electrolyte. Depar-ture of the gas bubbles can be accelerated by recirculating the electrolyte. This recircula-tion also evens the concentrarecircula-tion levels in the electrolyte, thus aiding to prevent addirecircula-tional overvoltages from occurring. Furthermore, the circulation of the electrolyte distributes heat more evenly (Zeng & Zhang 2010).

2.2.2 Bubble phenomena

Situation, in which forming gas bubbles in a water electrolysis system cannot be removed rapidly enough, can lead to high overpotential. Thus, identifying the effect that gas bubble formation has on energy consumption is essential in optimization of water electrolysis sys-tems. In water electrolysis, the formed bubble layer adjacent to electrode consists of two layers; 1) bubbles covering the electrode surface and 2) rising bubbles dispersing in elec-trolyte. On the electrode surface, bubbles grow gradually until a critical size is reached, which causes disengagement from the electrode surface. Bubbles absorbed on the anode and cathode cover active areas disturbing current distribution and reduce efficient areas (Wang et al. 2014). The gas bubbles on the surface of the electrodes locally increase the electrical resistance due to the lower conductivity of the gas with respect to the electrolyte.

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This decrease in electrical conductivity can be calculated using the approximation pro-posed by Bruggeman (Milewski et al. 2014)

𝜎_𝜀

𝜎₀ = (1 − 𝜀)^1.5, (2.14)

where σ0 is the conductivity in the bubble-free electrolyte, σε the conductivity in presence of gas bubbles, and ε the void fraction in the electrolyte. The void fraction—a measure of the volume of voids in the total volume of the electrolyte—of hydrogen and oxygen gas is proportional to the current, the diameter of the bubble, rising velocity of the bubble, and the geometry of the electrode (Tangphant et al. 2014). In alkaline water electrolysis, e.g.

the so-called zero-gap cell geometries can reduce the bubble formation and thus potentially improve the cell efficiency. In the zero-gap design, the distance between the electrode and the diaphragm is minimized (Hammoudi et al. 2012). Increasing the operating pressure will decrease the diameter of the bubbles, which increases the effective areas on the surface of the electrodes. Increasing the current density will increase the formation of bubbles, since according to the Faraday’s laws of electrolysis, the hydrogen production rate is directly proportional to the current.